JEE Advance - Physics (2011 - Paper 2 Offline - No. 14)
Explanation
In case A,
The capacitive reactance is
$$X_C^A = {1 \over {\omega C}}$$
Impedance of the circuit is
$${Z_A} = \sqrt {{{(R)}^2} + {{\left( {{1 \over {\omega C}}} \right)}^2}} $$
$$I_R^A = {V \over {\sqrt {{{(R)}^2} + {{\left( {{1 \over {\omega C}}} \right)}^2}} }}$$ ...... (i)
$$V_C^A = {{I_R^A} \over {\omega C}} = {V \over {\sqrt {{{(R\omega C)}^2} + 1} }}$$ ...... (ii)
In case B,
The capacitive reactance is
$$X_C^B = {1 \over {\omega (4C)}} = {1 \over {4\omega C}}$$
Impedance of the circuit is
$${Z_B} = \sqrt {{R^2} + {{\left( {{1 \over {4\omega C}}} \right)}^2}} $$
$$I_R^B = {V \over {\sqrt {{R^2} + {{\left( {{1 \over {4\omega C}}} \right)}^2}} }}$$ ..... (iii)
$$V_C^B = {V \over {\sqrt {{{(4R\omega C)}^2} + 1} }}$$ ..... (iv)
From (i) and (iii), we conclude that
$$I_R^A < I_R^B$$
From (ii) and (iv), we conclude that
$$V_C^A > V_C^B$$
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